R/update_beta_sparse_ncv.R

In jocelynchi/L2E-package-demo: Robust Structured Regression via the L2 Criterion

#' Beta update in L2E sparse regression - NCV
#'
#' \code{update_beta_sparse_ncv} updates beta for L2E sparse regression using existing penalization methods
#'
#' @param y Response vector
#' @param X Design matrix
#' @param beta Initial vector of regression coefficients
#' @param tau Initial precision estimate
#' @param lambda Tuning parameter
#' @param penalty Available penalties include lasso, MCP and SCAD.
#' @param max_iter Maximum number of iterations
#' @param tol Relative tolerance
#' @return Returns a list object containing the new estimate for beta (vector) and the number of iterations (scalar) the update step utilized
#' @importFrom Matrix Diagonal
#' @importFrom ncvreg ncvfit
#'
update_beta_sparse_ncv <- function(y,X,beta,tau,lambda, penalty, max_iter=1e2,tol=1e-4) {

  n <- nrow(X)

  for (i in 1:max_iter) {

    beta_last <- beta
    Xbeta <- X %*% beta
    r <- y - Xbeta
    w <- as.vector(exp(-0.5* (tau*r)**2 ))


    W <- Diagonal(n=n, x = sqrt(as.vector(w)))
    Xtilde <- as.matrix(W%*%X)
    ytilde <- as.vector(W%*%y)
    beta <- as.vector(ncvfit(Xtilde, ytilde, init = beta_last, penalty=penalty,lambda = lambda,
                             max.iter = 100, warn = FALSE)$beta)

    if (norm(as.matrix(beta_last-beta),'f') < tol*(1 + norm(as.matrix(beta_last),'f'))) break
  }

  return(list(beta=beta,iter=i))
}